What were the fundamental grounds of the struggle between the Persians and the Greeks?

Although some Greeks (as can be seen in Aeschylus's play The Persianssaw the Persian Wars as a struggle between democracies and monarchies, or between freedom and slavery, these wars were truly about power.

By the mid-sixth century BCE, the Persian Empire and the Greek city states had grown enough that they came in contact with one another. Greek city states in Asia Minor fell under the control of the Persians. In 499 BCE, though, some of these city states rebelled, trying to become independent from Persia. The Athenians helped these rebellions along, which led to Darius's decision to invade mainland Greece.

Thus, the real basis for the war was a desire for power and a degree of what we might call nationalism. Greeks came to the aid of other Greeks and then the Greeks and the Persians fought in an attempt to establish whether Greece would come to be dominated by Persia. This was not really a war about democracy resisting tyranny. Instead, it was about one state trying to conquer another group of states. In other words, it was about power.